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Differentiating each term separately, and using implicit differentiation to differentiate the functions of y by differentiating with respect to y and multiplying by dy/dx, we can obtain 6y dy/dx + ln2 2^x + ...

y = arctan(x)tan(y) = xsec 2 (y) = dx/dyfrom cos 2 A + sin 2 A = 1, we know that 1 + tan 2 A = sec 2 A (divide by cos 2 A), so we substitute in1 + tan 2 (y) = dx/dyfrom the initial relationship,1 + x 2 = dx/...

This indefinite integral (has no defined limits) should be evaluated by integration by substitution This is because you cannot integrate sin 2 xWhen doing integration by substitution, the first thing we need...

This can be done with integration by substitution. If we let u=tanx then du/dx=sec^2(X). If we substitute U into the integrand we get it being u(sec^2(X))dx. rearranging the du/dx equation to make dx the sub...

To start with, we want to put this into quadratic form, where we have ax^2+bx+c=0. We notice that there are terms on both sides of the equation. So we can expand the right hand side and then bring all the te...